The following table shows the number of patients of different age . . .

Question : The following table shows the number of patients of different age group who were discharged from the hospital in a particular month : 

Age (in years)	Number of Patients Discharged
5-15	6
15-25	11
25-35	21
35-45	23
45-55	14
55-65	5
Total	80

Find the 'mean' and the 'mode' of the above data.

CBSE 2025

Solution : 

Mean 

Age (in years) C.I.	No. of Patients Discharged (fi)	xi	di=xi-a	ui=di/h	fiui
5-15	6	10	-20	-2	-12
15-25	11	20	-10	-1	-11
25-35	21	30=a	0	0	0
35-45	23	40	10	1	23
45-55	14	50	20	2	28
55-65	5	60	30	3	15
	Σfi=80				Σfiui=43

Mean by Step Deviation Method 
Mean (x̄) = a+[Σf_iu_i/Σf_i]×h
x̄ = 30+[43/80]×10
=30+[43/8]
=30+5.375
=35.375
=35.38 (approx)

Mean age of the patients who got discharged is 35.38 years.

Mode 

Age (in years)	Number of Patients Discharged
5-15	6
15-25	11
25-35	21 - f0
35-45	23 - f1
45-55	14 - f2
55-65	5
Total	80

Here
Maximum Frequency = 23
So, Modal Class = 35-45
Lower Limit (l) = 35
Class Size (h) = 45-35 = 10

Mode = l+[(f₁-f₂)/(2f₁-f₀-f₂)]×h
Mode = 35+[(23-21)/(2×23-21-14)]×10
Mode = 35+[2/(46-35)]×10
Mode = 35+[2/11]×10
Mode = 35+20/11
Mode = 35+1.818
Mode = 36.818
Mode = 36.82 (approx)

Hence, the modal age of the patient discharged from the hospital is 36.82 years.